A244470 Maximal term in row n of sequence A240388 when regarded as a triangle.

1, 1, 2, 4, 6, 9, 17, 25, 40, 72, 106, 169, 305, 449, 716, 1292, 1902, 3033, 5473, 8057, 12848, 23184, 34130, 54425, 98209, 144577, 230548, 416020, 612438, 976617, 1762289, 2594329, 4137016, 7465176, 10989754, 17524681, 31622993, 46553345

Offset: 2

Author

N. J. A. Sloane, Jul 01 2014

Keywords

• nonn
• easy

Links

• J. Lansing, Largest Values for the Stern Sequence, J. Integer Seqs., 17 (2014), #14.7.5.
• Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,1).

Crossrefs

Cf. A002487, A240388.

Trisections: A001076, A048875.

Programs

Maple

A244470 := proc(n)
    coeftayl( (x^2+x^3+2*x^4+2*x^6+x^7+2*x^10)/(1-4*x^3-x^6),x=0,n) ;
end proc:
seq(A244470(n), n=1..50) ; # R. J. Mathar, Jul 05 2014

Mathematica

CoefficientList[Series[(1 + x + 2*x^2 + 2*x^4 + x^5 + 2*x^8)/(1 - 4*x^3 - x^6), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jul 05 2014 *)
LinearRecurrence[{0,0,4,0,0,1},{1,1,2,4,6,9,17,25,40},40] (* Harvey P. Dale, Apr 08 2015 *)

Formula

G.f.: (x^2+x^3+2*x^4+2*x^6+x^7+2*x^10)/(1-4*x^3-x^6).

a(3*n-1) = A001076(n). a(3*n) = A048875(n-1). - R. J. Mathar, Jul 05 2014

a(n) = 4*a(n-3) + a(n-6). - Harvey P. Dale, Apr 08 2015

a(3*n+1) = 2*Lucas(3*n-3) + Fibonacci(3*n-3)/2 for n>1. - Greg Dresden, Oct 17 2021